Subgroups — #67006

Order 352.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊D₁₁	C₂	1	3	yes	maximal, complemented
3	C₂²⋊Dic₁₁	C₂	1	3	yes	maximal, complemented
4	C₂³×C₁₁	—	2	6	no	—
5	C₂³×C₁₁	C₂²	1	3	yes	—
6	C₂²×D₁₁	C₂²	1	1	yes	characteristic, complemented
7	C₂²⋊D₁₁	—	2	6	no	—
8	C₂×Dic₁₁	C₂²	1	3	yes	complemented
9	C₂²×C₁₁	—	2	8	no	—
10	C₂²×C₁₁	—	2	6	no	—
11	C₂²×C₁₁	D₄	1	6	yes	complemented
12	C₂²×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×D₁₁	—	2	3	no	—
14	Dic₁₁	—	2	3	no	—
15	#120	—	11	1	no	maximal, Sylow
16	C₂×C₁₁	—	2	6	no	—
17	C₂×C₁₁	C₂×D₄	1	3	yes	—
18	D₁₁	—	4	1	no	—
19	C₂⁴	D₁₁	1	1	yes	characteristic, complemented
20	C₂×D₄	—	11	3	no	—
21	C₂²⋊C₄	—	11	3	no	—
22	C₁₁	#120	1	1	yes	characteristic, complemented, Sylow
23	C₂³	—	2	6	no	—
24	C₂³	—	11	1	no	—
25	C₂³	C₂×D₁₁	1	3	yes	—
26	D₄	—	22	6	no	—
27	C₂×C₄	—	11	3	no	—
28	C₂²	—	2	8	no	—
29	C₂²	—	2	6	no	—
30	C₂²	—	22	3	no	—
31	C₂²	C₂²⋊D₁₁	1	6	yes	complemented
32	C₂²	C₂²×D₁₁	1	1	yes	characteristic
33	C₄	—	22	3	no	—
34	C₂	—	2	6	no	—
35	C₂	—	44	1	no	—
36	C₂	C₂×C₂²⋊D₁₁	1	3	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.